UPPER BOUNDS FOR RUIN PROBABILITY IN A CONTROLLED GENERAL RISK PROCESS WITH RATE OF INTEREST IS A FIRST - ORDER

Abstract

In this paper, we study a controlled general risk process where claim is homogeneous Markov
chain and rate of interest is a first-order autoregressive process. We assume that claim is
homogeneous Markov chain, take a countable number of nonnegative values and rate of interest
is a sequence of non-negative random variables what it satifies a first-order autoregressive
process. Generalized Lundberg inequalities for ruin probability of this process are derived by
the Martingale approach.